Getting an imported object's name
You can use Python set operations.


Make a set from all objects in the scene before the import
Perform the import
Make another set from all objects and subtract the set you made earlier


The only objects left in the set are the ones that were imported.

old_objs = set(context.scene.objects)
bpy.ops.import_scene.fbx(filepath="/home/simon/untitled.fbx")
imported_objs = set(context.scene.objects) - old_objs

print("Imported:", imported_objs)